Advertisements
Advertisements
प्रश्न
Find the nth derivative of the following : cos x
Advertisements
उत्तर
Let y = cos x
Then `"dy"/"dx" = "d"/"dx"(cosx)`
= `-sinx`
= `cos(pi/2 + x)`
`(d^2y)/(dx^2) = "d"/"dx"(-sinx)`
= `-cosx`
= cos(π + x)
= `cos((2pi)/2 + x)`
`(d^3y)/(dx^3) = "d"/"dx"(-cosx)`
= `-"d"/"dx"(cosx)`
= – ( – sin x)
= sin x
= `cos((3pi)/2 + x)`
In general, the nth order derivative is given by
`(d^ny)/(dx^n) = cos((npi)/2 + x)`.
APPEARS IN
संबंधित प्रश्न
Find `bb(dy/dx)` in the following:
2x + 3y = sin y
Find `bb(dy/dx)` in the following:
x3 + x2y + xy2 + y3 = 81
Find `bb(dy/dx)` in the following:
sin2 x + cos2 y = 1
Find `bb(dy/dx)` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
Show that the derivative of the function f given by
If \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\]
, find f'(4).
Write the derivative of f (x) = |x|3 at x = 0.
Let \[f\left( x \right)\begin{cases}a x^2 + 1, & x > 1 \\ x + 1/2, & x \leq 1\end{cases}\] . Then, f (x) is derivable at x = 1, if
Find `dy/dx if x^3 + y^2 + xy = 7`
Find `(dy)/(dx) if y = cos^-1 (√x)`
Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`
If x = `(t + 1)/(t - 1), y = (t - 1)/(t + 1), "then show that" y^2 + "dy"/"dx"` = 0.
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
Differentiate `cos^-1((1 - x^2)/(1 + x^2)) w.r.t. tan^-1 x.`
Differentiate `tan^-1((cosx)/(1 + sinx)) w.r.t. sec^-1 x.`
Differentiate xx w.r.t. xsix.
Find `(d^2y)/(dx^2)` of the following : x = a(θ – sin θ), y = a(1 – cos θ)
If x = cos t, y = emt, show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" - m^2y` = 0.
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
Find the nth derivative of the following:
`(1)/x`
Find the nth derivative of the following : apx+q
Find the nth derivative of the following : sin (ax + b)
Choose the correct option from the given alternatives :
Let `f(1) = 3, f'(1) = -(1)/(3), g(1) = -4 and g'(1) =-(8)/(3).` The derivative of `sqrt([f(x)]^2 + [g(x)]^2` w.r.t. x at x = 1 is
Choose the correct option from the given alternatives :
If y = sec (tan –1x), then `"dy"/"dx"` at x = 1, is equal to
If x sin (a + y) + sin a . cos (a + y) = 0, then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
If sin y = x sin (a + y), then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
DIfferentiate `tan^-1((sqrt(1 + x^2) - 1)/x) w.r.t. tan^-1(sqrt((2xsqrt(1 - x^2))/(1 - 2x^2)))`.
If y2 = a2cos2x + b2sin2x, show that `y + (d^2y)/(dx^2) = (a^2b^2)/y^3`
Find `"dy"/"dx"` if, yex + xey = 1
Find `"dy"/"dx"` if, `"x"^"y" = "e"^("x - y")`
Choose the correct alternative.
If y = 5x . x5, then `"dy"/"dx" = ?`
Choose the correct alternative.
If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2` then `"dy"/"dx"` = ?
If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`
If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`
Find `"dy"/"dx"` if x = `"e"^"3t", "y" = "e"^(sqrt"t")`.
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
y = `e^(x3)`
If y = `sqrt(tan x + sqrt(tanx + sqrt(tanx + .... + ∞)`, then show that `dy/dx = (sec^2x)/(2y - 1)`.
Find `dy/dx` at x = 0.
`"If" log(x+y) = log(xy)+a "then show that", dy/dx=(-y^2)/x^2`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx if , x = e^(3t) , y = e^sqrtt`
Find `dy/dx` if, x = e3t, y = `e^sqrtt`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
If log(x + y) = log(xy) + a then show that, `dy/dx=(-y^2)/x^2`
